Use this tag for questions about free modules and related notions as projective modules or free abelian groups. This tag should be used together with the tags of abstract algebra and modules.

In abstract algebra, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. On the other hand, free abelian groups are precisely the free modules over the ring $\Bbb Z$.